Quantum states with continuous spectrum for a general time-dependent oscillator

We investigated quantum states with continuous spectrum for a general time-dependent oscillator using invariant operator and unitary transformation methods together. The form of the transformed invariant operator by a unitary operator is the same as the Hamiltonian of the simple harmonic oscillator:I’ = p²/2 +ω ² q ²/2. The fact thatω ² of the transformed invariant operator is constant enabled us to investigate the system separately for three cases, whereω ² > 0,ω ² < 0, andω ² = 0. The eigenstates of the system are discrete forω ² > 0. On the other hand, forω ² <− 0, the eigenstates are continuous. The time-dependent oscillators whose spectra of the wave function are continuous are not oscillatory. The wave function forω ² < 0 is expressed in terms of the parabolic cylinder function. We applied our theory to the driven harmonic oscillator with strongly pulsating mass.     

Field-induced anomalies of the polariton spectrum of a bounded crystal with spatial dispersion: I. A semi-infinite crystal

Conditions are determined under which an external magnetic field leads to a new mechanism of formation of surface TM polaritons in crystals possessing dynamic magnetoelectric interaction and spatial dispersion simultaneously.     

Localized phonon states at the edge of the continuous spectrum

An analysis is made of the influence of defects on the averaged Green’s function of optical phonons whose imaginary part is proportional to the cross section for Raman one-phonon light scattering, which depends on the frequency transfer. A variant of the “cross” technique which can take into account the localized states at defects is used. The defects are assumed to be two-dimensional (of the dislocation type) at which localized states exist near the edge of the continuous spectrum interacting weakly with the defect. As a result of this interaction, which depends on the defect concentration, the states of the continuous spectrum are shifted and broadened, the inhomogeneous broadening depending strongly on the frequency transfer (phonon density of states effect), which leads to asymmetry of the Raman line. The defect concentration also influences the localized states which interact mainly via band states.     

Hydrodynamics of reactive systems: Chemical reactions near the critical points

The rate of a chemical reaction is expressed in terms of the correlation functions which are found from the full system of hydrodynamic equations in reactive systems. In the limiting cases one obtains all three types of behavior of reaction rates near the critical points found in experiments (slowing-down, speeding-up, insensitivity to criticality). This behavior depends on the number of reactive and inert components in a system, proximity and path of approach to the critical point.     

Cluster description of water-in-oil microemulsions near the critical and percolation points

The three-component ionic microemulsion system consisting of AOT/water/decane shows an unusual phase behavior in the vicinity of room temperature. The phase diagram in the temperature-volume fraction (of the dispersed phase) plane exhibits a lower consolute critical point at about 40 degrees centigrades and 10% volume fraction. A percolation line, starting from the vicinity of the critical point, cuts across the plane, extending to high volume fraction side at progressively lower temperatures. In this paper we review the evidence that allows to interpret the phase behavior of our system in terms of interacting spherical droplets. We also investigate the dynamics of droplets, below and approaching the critical point by dynamic light scattering. The first cumulant and time evolution of the droplet density correlation function can be quantitatively calculated by assuming the existence of polydispersed fractal clusters formed by the microemulsion droplets due to attraction. The relaxation phenomena observed in an extensive set of measurements of electrical conductivity and permittivity close to percolation is also reviewed and interpreted through the same cluster-forming mechanism, which reproduces the most relevant features of the frequency-dependent complex dielectric constant of this system. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Fluid molecule oscillations and the continuous spectrum near the rayleigh line

Of late there have been considerable developments in the theoretical study of the contour of spectral lines and the Rayleigh line by general statistical methods in the theory of random processes. On the basis of the general equations describing the rotational motion of molecules [1,2], and also of the equation which describes the change in the projection of the dipole moment onto the laboratory coordinate axes [3], we seek a correlation function whose Fourier transform leads finally to the required spectral distribution. In the present article we solve the problem of the spectral distribution by a direct analysis of the change in the projection onto the laboratory coordinate axes of the dipole moment induced in a molecule by an incident light wave. We consider a specific model for the rotational motion of fluid molecules.     

Resonant Mandelstam-Brillouin light scattering and Raman scattering in semiconductors with intermediate exciton states belonging to discrete exciton bands and the continuous spectrum

The results of a theoretical and experimental investigation of resonant Mandelstam-Brillouin light scattering by thermal acoustic phonons with k=0 near the direct absorption edge (in the case of ZnSe crystals) are analyzed. The appearance of a new type of resonant increase in the intensity of Raman scattering by optical phonons with k≠0, which corresponds to resonance with the scattered light in the output channel, near the indirect absorption edge (in the case of semi-insulating GaP:N crystals) is also reported. The resonant gain reaches ∼4×10³ at frequencies corresponding to overtone scattering assisted by LO(X) and LO(L) phonons. Exciton states belonging to both discrete exciton bands and to the continuous spectrum are considered as the intermediate states involved in the scattering processes in calculations of the resonant scattering tensors. In addition, all the intraband transitions, as well as the interband transitions between the conduction band, the valence bands, and the spin-orbit split-off band are taken into account, and good agreement with the experimental results is obtained. Fiz. Tverd. Tela (St. Petersburg) 40, 938–940 (May 1998)     

Landau-Zener transition of a two-level system driven by spin chains near their critical points

The Landau-Zener (LZ) transition of a two-level system coupling to spin chains near their critical points is studied in this paper. Two kinds of spin chains, the Ising spin chain and XY spin chain, are considered. We calculate and analyze the effects of system-chain coupling on the LZ transition. A relation between the LZ transition and the critical points of the spin chain is established. These results suggest that LZ transitions may serve as the witnesses of criticality of the spin chain. This may provide a new way to study quantum phase transitions as well as LZ transitions.     

Field-induced anomalies of the polariton spectrum of a bounded crystal with spatial dispersion: II. Crystal plate

Conditions are determined under which an external magnetic field leads to anomalies in the spectrum of bulk TM polaritons in a crystal plate possessing simultaneously the dynamic magnetoelectric effect and spatial dispersion.     

Phase equilibria,metastable states,and critical points in a simple one-component system

Stability of metastable phase states against infinitesimal perturbations in a simple one-component system is considered. The method of molecular dynamics simulation was used to determine the boundaries of essential instability of supersaturated vapor, a superheated liquid, and a superheated crystal. The absence of a spinodal from a supercooled liquid and the dependence of the boundary of essential instability of a superheated crystal on the character of deformation were established. It is shown that each of the three lines of phase equilibria in a one-component system has an endpoint of termination of phase coexistence. As distinct from the liquid–gas critical point, which is the point of phase identity and is located in the region of stable states, the endpoints of melting and sublimation lines are located in the region ofmetastable states. At these points, a critical (spinodal) state is achieved only for one of the coexisting phases.     

Broadening peculiarities of vibrational bands in the spectrum of carbon dioxide close to the critical temperature

Carbon dioxide Fermi doublet 1388/1285 cm⁻¹ Q-band broadenings and shifts measured using coherent anti-Stokes Raman spectroscopy are presented. Measurements were performed over a wide density range (0.1ρ _c < ρ < 1.9ρ _c ) during compression in the gaseous and condensed states at temperatures close to critical (the reduced temperature values were T _r = 0.995, 1.000, and 1.006). At densities above the ρ _c critical value, the width of Q-bands did not increase as the density grew, and the low-frequency Q band considerably narrowed up to the density value 1.7ρ _c . The main reason for this anomalous behavior was progressing narrowing of the spectral contribution caused by the special features of rotational exchange in the condensed state and not related directly to the closeness to the critical point. The refined critical broadening value was about 10% of the width for the high-frequency Q-band and 15% of the width for the low-frequency Q-band.     

The influence of critical points on polariton dispersion in the band of two-particle states

The presence of critical points in the two-phonon band in conditions of the Fermi resonance on a polariton may result in a considerable polariton dispersion inside the band of two-particle states. Moreover, the polariton linewidth, conditioned by the decay into two particles, is shown to become zero near critical points; this fact holds certain promise for the determination of the positions of critical points in side the band of two-particle states.     

Renormalization group study of quantum fluctuations near classical critical points of Hamiltonian systems

A general framework is considered for treating quantum corrections to the classical limit in the Wigner function formalism. We discuss the quantal effect on the classical phenomena such as period doubling and the breakup of KAM tori. By using an exact renormalization group method, the scaling factor for Planck's constant is derived as an eigenvalue of the linearized renormalization transformation.     

Localized electron states in the continuous spectrum of the Cu(001) monolayer

The results of the calculation of electron bands of bound states that cross the edge of the continuous spectrum for the (001) fcc copper monolayer are presented for the first time. The calculations are performed in the local approximation for the exchange and correlations using the film variant of the Green’s function technique. Symmetry of electron states near the edge of the continuous spectrum is explored. It is found that there are bound states along the $ \bar \sum $ \bar \sum direction of the two-dimensional Brillouin zone of the Cu(001) monolayer that are embedded in the continuum of delocalized states of the continuous spectrum. Along the $ \bar \Delta $ \bar \Delta and $ \bar Y $ \bar Y directions, bands of bound states turn into resonance states after crossing the edge of the continuous spectrum.     

Temperature dependence of the upper critical field in the model of a superconductor with singular points near the Fermi surface

We consider a generalization of BCS theory to the case where the energy spectrum of parent charge carriers near the Fermi energy has a nonlinear character. This nonlinearity can cause an abrupt decrease in the coherence length, growth of the density of states and transition temperature, and non-analyticity of the vertex part as a function of the momentum. As the density of states increases the model exhibits a tendency toward negative curvature of the critical field at the transition point (although a sign change of the curvature is possible near it). Positive curvature can show up upon depletion of the density of states, which in fact corresponds to a departure of the crystal parameters from the conditions maximizing the transition temperature. Fiz. Tverd. Tela (St. Petersburg) 41, 975–978 (June 1999)     

Numerical trajectory simulation and radiation spectrum of relativistic particles moving in a crystal near a crystallogrpahic plane

We study the radiation spectra of relativistic particles in a crystal by numerically simulating the trajectories for the case where the particles move near crystallographic planes. We give formulas for the simulation of the polarization characteristics of the radiation. The results are compared with the radiation for motion about a crystallographic axis and with experimental data.     

Resonance fluorescence spectrum of a three-level atom

We consider the excitation spectrum arising from the interaction between a three-level atom and a strong electromagnetic field in the frequency region where the two atomic transition frequencies are nearly equal to once and twice the frequency of the pump field respectively. Detailed expressions for the spectral functions are derived describing the two-, one- and zero-photon excitations as well as those arising from the coupling between them, in the limit of high photon densities. The zero-photon excitations describe low frequency modes induced by the pump field under resonance conditions.